The reason why this Universe has three dimensional space and 1 dimensional time is because that’s how a four dimensional hypersphere Black Hole, or its later avatar Big Bang, embedded in higher 5 or 6 dimensions, exploded and created this Universe.
This Universe is 3+1 dimensional because that is how it was originated from almost a singularity. The dimension of this Universe should be directly correlated with that of the singularity.
Now four spatial dimensional Universes having human life is possible and humans evolved in four dimensions should be more complex and more intelligent than those in three.
Universes having more than four spatial dimensions are possible but they cannot support life for longer time because somewhere in those planets in those Universes where evolution of biological life is possible, the genesis would be so complex that it could hurt sequences in biological and psychological evolutions.
It could be more or less like truncated evolution. The evolution being so complicated there that humans may not evolve and if they evolve then they may not survive for long.
Also, proper human procreation may not be possible in higher or lower spatial dimensions as compared to that in three. Enjoying sex requires minimum of three spatial dimensions: and that is particularly true of humans as transformation to bipod form from quadripod is the biggest sexual revolution till to date on earth.
If conjectured then humans living in four spatial dimensions could enjoy sex as good as humans on earth or may be even better, but not in higher spatial dimensions.
Therefore, Universes having spatial dimension less than or equal to two and also more than four, may not support complex biological species. The four dimensional biological species would be more intelligent than those in three and they in turn would be more complex than those in two. There is no question of biological micro-organism being there in one dimensional world.
Now time can have one or two dimension in human-habitat Universes, if only integral dimensions are considered and fractals not. But they cannot have less than one or more than two in life supporting Universes.
Less than one there cannot have biology and more than two spatial dimensions would crunch the human civilizations with humans there being unable to comprehend and they ultimately collapsing because of senses’ conflicts with brains.
The psychology probably cannot be supported in Universe having more than four spatial dimensions and two time dimensions. There just cannot be much complex psychology in two spatial dimensional Universe, even if somehow life is able to evolve there. Again species living in Universe having two time dimensions would be more complex than those in one dimensional time.
Therefore, the possible dimensions in Universe supporting life are 3+1, 3+2, 4+1 and 4+2, though not equally probable. Still the preferred dimension of the Universes is 3+1 because R4 space is dual in the sense that it breaks up into two different topologically space-time curvature at very small length; at Plank’s length, and at very big length; at the size of the Universe. R3 and R5 or even R6 just cannot.
The duality of R4 space allows the quantum phenomenon to take place and also allows non-conservation and interaction at small space-time and conservation at the level of Universe, except those of information and entropy.
As of now entropy is increasing and information decreasing; they are inversely related. But time-dependent topological fractal additions and subtractions to dimensions of R4 Universes are possible.
It should be noted that Charge Parity Time invariance (CPT) theorem could be preserved at dimensions differing fractally from four. Sure, the R5, R6 etc space-time can have unique features; something that R4 space-time does not have and few among them can have human life supporting conditions.
Sure, if biological lives are not factor then there cannot be much constraint on the dimensions of the possible Universes though all possibilities just cannot be equally probable.